Current Induced Faceting in Theory and Simulation

Abstract
We consider the effect that a directed migration of adatoms, such as that which arises due to an externally applied electric field, has over the morphology of a crystal surface. Applying linear stability arguments to a continuum model we find that the stability of a surface is determined by the dependence of the adatom mobility on the surface orientation. In one dimension, surfaces may be either stable or unstable. In two dimensions however, we find that a surface of general orientation is always unstable. These results are confirmed by computer simulations of solid-on-solid models, which also show late time coarsening behaviour in cases of surface instability, such that the typical domain size is seen to increase as a power law of the simulation time. Our numerical data demonstrate a growth exponent 1/4 in one dimension and 1/2 in two dimensions, which can be supported by the continuum theory.